Answer:
The Linear equation: V (x) = 21,000 - 2000x
Where V = Value of Car after a time period ($)
x = Number of years (yrs)
Value of Car after 8 years = $5,000
Step-by-step explanation:
Let the value of the car and the number of years be related by the Linear equation :
V(x) = Mx +C-------------------------------------------- (1)
Where V =Value of Car after a time period ($)
x = Number of years (yrs)
M = Slope of the linear relationship
C = The intercept of the straight line on the value axis
From the question two different coordinates of Value and the number of years where given: (V₁ ,x₁) and (V₂ ,x₂)
First coordinate (V₁ ,x₁) = ($15,000 , 3)
Second coordinate (V₂ ,x₂) = ($11,000, 5)
These can be substituted into equation (1) and (2) to calculate the for M & C
Substituting the first coordinate into (1) we have :
15,000 = 3M +C-----------------------------------------------------------------(2)
Substituting the second coordinate into (1) we have :
11,000 = 5M +C------------------------------------------------------------------(3)
Solving equation (2) and (3) simultaneously using elimination method, we have:
15,000 = 3M +C
11,000 = 5M +C
4000 = -2M
M = -2000
Substituting the value of M into equation (3) we have:
11,000 = 5M +C
11,000 = 5(-2000) +C
11,000 = -10,000 +C
C =21,000
Substituting the value of M and C into equation (1), we have the Linear relationship for Value and the number of years
V (x) = -2000x + 21,000---------------------------------------------------------------- (4)
V (x) = 21,000 - 2000x ---------------------------------------------------------------- (5)
Substituting x = 8 years into equation (5) we have:
V (x) = 21,000 - 2000x
= 21000 - 2000 (8)
= 21000 - 16000
= $5000
